A rigorous generation of spin-adapted (spin-free) substitution operators for high spin (S = Sz) references of an arbitrary substitution order and spin quantum number S is presented. The generated operators lead to linearly independent but non-orthogonal configuration state functions (CSFs) when applied to the reference and span the complete spin space. To incorporate spin completeness, spectating substitutions (e.g., Êivva) are introduced. The presented procedure utilizes Löwdin's projection operator method of spin eigenfunction generation to ensure spin completeness. The generated operators are explicitly checked for (i) their linear independence and (ii) their spin completeness for up to tenfold substitutions and up to a multiplicity of 2S + 1 = 11. A proof of concept implementation utilizing the generated operators in a coupled cluster (CC) calculation was successfully applied to the high spin states of the boron atom. The results show pure spin states and small effects on the correlation energy compared to spin orbital CC. A comparison to spin-adapted but spin-incomplete CC shows a significant spin-incompleteness error.SABRE (Signal Amplification By Reversible Exchange) has become a widely used method for hyper-polarizing nuclear spins, thereby enhancing their Nuclear Magnetic Resonance (NMR) signals by orders of magnitude. In SABRE experiments, the non-equilibrium spin order is transferred from parahydrogen to a substrate in a transient organometallic complex. The applicability of SABRE is expanded by the methodology of SABRE-relay in which polarization can be relayed to a second substrate either by direct chemical exchange of hyperpolarized nuclei or by polarization transfer between two substrates in a second organometallic complex. To understand the mechanism of the polarization transfer and study the transfer efficiency, we propose a theoretical approach to SABRE-relay, which can treat both spin dynamics and chemical kinetics as well as the interplay between them. The approach is based on a set of equations for the spin density matrices of the spin systems involved (i.e., SABRE substrates and complexes), which can be solved numerically. Using this method, we perform a detailed study of polarization formation and analyze in detail the dependence of the attainable polarization level on various chemical kinetic and spin dynamic parameters. We foresee the applications of the present approach for optimizing SABRE-relay experiments with the ultimate goal of achieving maximal NMR signal enhancements for substrates of interest.We studied the effect of self-interaction error (SIE) on the static dipole polarizabilities of water clusters modeled with three increasingly sophisticated, non-empirical density functional approximations (DFAs), viz., the local spin density approximation (LDA), the Perdew-Burke-Ernzerhof (PBE) generalized-gradient approximation (GGA), and the strongly constrained and appropriately normed (SCAN) meta-GGA, using the Perdew-Zunger self-interaction-correction (PZ-SIC) energy functional in the Fermi-Löwdin orbital SIC framework. Our results show that while all three DFAs overestimate the cluster polarizabilities, the description systematically improves from LDA to PBE to SCAN. The self-correlation free SCAN predicts polarizabilities quite accurately with a mean absolute error (MAE) of 0.53 bohr3 with respect to coupled cluster singles and doubles (CCSD) values. Removing SIE using PZ-SIC correctly reduces the DFA polarizabilities, but overcorrects, resulting in underestimated polarizabilities in SIC-LDA, SIC-PBE, and SIC-SCAN. Finally, we applied a recently proposed locally scaled SIC (LSIC) method using a quasi self-consistent scheme and using the kinetic energy density ratio as an iso-orbital indicator. The results show that the LSIC polarizabilities are in excellent agreement with mean absolute errors of 0.08 bohr3 for LSIC-LDA and 0.06 bohr3 for LSIC-PBE with most recent CCSD polarizabilities. Likewise, the ionization energy estimates as absolute of highest occupied energy eigenvalue predicted by LSIC are also in excellent agreement with CCSD(T) ionization energies with MAEs of 0.4 eV for LSIC-LDA and 0.06 eV for LSIC-PBE. The LSIC-LDA predictions of ionization energies are comparable to the reported GW ionization energies, while the LSIC-PBE ionization energies are more accurate than the reported GW results.Density functional theory is widely used for modeling the magnetic properties of molecules, solids, and surfaces. Rung-3.5 ingredients, based on the expectation values of nonlocal one-electron operators, are new promising tools for the construction of exchange-correlation functional approximations. We present the formal extension of rung-3.5 ingredients to the calculation of magnetic properties. We add to the underlying nonlocal operators a dependence on the gauge of the magnetic field, and we derive the working equations for rung-3.5 expectation values in basis sets of gauge-including atomic orbitals. We demonstrate that the gauge corrections are significant. We conclude with an initial study of chemical shifts, optical rotatory dispersion, and Raman optical activity spectra predicted by M11plus, a range-separated hybrid meta functional incorporating nonlocal rung-3.5 correlation. https://www.selleckchem.com/products/pf-04418948.html M11plus proves to be reasonably accurate, further motivating the incorporation of nonlocal rung-3.5 ingredients in new density functional approximations.Concurrent multiscale techniques such as Adaptive Resolution Scheme (AdResS) can offer ample computational advantages over conventional atomistic (AT) molecular dynamics simulations. However, they typically rely on aphysical hybrid regions to maintain numerical stability when high-resolution degrees of freedom (DOFs) are randomly re-inserted at the resolution interface. We propose an Energy Minimized AT (DOF) Insertion (EMATI) method that uses an informed rather than random AT DOF insertion to tackle the root cause of the issue, i.e., overlapping AT potentials. EMATI enables us to directly couple AT and coarse-grained resolutions without any modifications of the interaction potentials. We exemplify AdResS-EMATI in a system of liquid butane and show that it yields improved structural and thermodynamic properties at the interface compared to competing AdResS approaches. Furthermore, our approach extends the applicability of the AdResS without a hybrid region to systems for which force capping is inadequate.